These days, mathematical modeling and simulations are used for designing engineering equipment in almost all industries. Numerical optimization algorithms are incorporated into the modeling and simulation process to design optimal performance engineering equipment. The main goal of the design process is to ensure all product specifications consider variability and uncertainty in the design response [1]}, [2]}. A class of uncertainties originating from system variability, such as boundary conditions used in the mathematical modeling, input parameters (temperature, load, fluid, and material densities), etc, are called aleatory uncertainties. Variability, uncertainty, and tolerance must be incorporated into the system design process to assure the quality and reliability of the design. Therefore, optimal product parameters where the system behavior is robust despite unavoidable variability must be evaluated. In the early design process of a product, a robust optimization process is a new, cost-effective and innovative approach that allows to include uncertainties in the optimization process. From the modeling perspective, it is also necessary to understand the engine performance near or around the optimal point in the design process. For example, in designing a jet engine with maximum engine efficiency, one needs to include variations in operating conditions, geometry roughness/ tolerances, and uncertainties in the material properties as the engine will not operate strictly at the optimal points but at nearby points also. Hence, the goal is to maximize efficiency while ensuring the engine doesn't fail the emission requirements, and this process ensures that engine efficiency is also acceptable for the known uncertainties.
